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FRM Part I · FRM Exam Part I · Introduction to Derivatives

A fund holds a long forward on 10,000 ounces of gold with delivery price USD 1,900. Two months before maturity, the forward price for the same maturity is USD 1,960 and the continuously compounded risk-free rate is 6% per year. What is the approximate value of the long position (PV of forward price difference times quantity)?

The long forward value is the discounted difference between the current forward price and the delivery price, times the quantity: 60 x e^(-0.01) x 10,000, about USD 594,000. Failing to discount gives USD 600,000, which overstates the value.

  1. AUSD 600,000
  2. BUSD 594,000Correct
  3. CUSD 606,000
  4. DUSD 59,400

Explanation

Value = (F - K) x e^(-rT) x quantity = 60 x e^(-0.06 x 2/12) x 10,000. e^(-0.01) = 0.990050, so 60 x 0.99005 = 59.403; times 10,000 = about USD 594,030. Ignoring discounting gives 600,000, and compounding upward gives 606,000.

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